On the stability of kalman-bucy diffusion processes

Bishop, AN; Del Moral, P

On the stability of kalman-bucy diffusion processes

Bishop, AN

Del Moral, P

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Publication Type:: Journal Article
Citation:: SIAM Journal on Control and Optimization, 2017, 55 (6), pp. 4015 - 4047
Issue Date:: 2017-01-01

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Field	Value	Language
dc.contributor.author	Bishop, AN https://orcid.org/0000-0001-8581-8562	en_US
dc.contributor.author	Del Moral, P	en_US
dc.date.issued	2017-01-01	en_US
dc.identifier.citation	SIAM Journal on Control and Optimization, 2017, 55 (6), pp. 4015 - 4047	en_US
dc.identifier.issn	0363-0129	en_US
dc.identifier.uri	http://hdl.handle.net/10453/127196
dc.description.abstract	© 2017 Society for Industrial and Applied Mathematics. The Kalman-Bucy filter is the optimal state estimator for an Ornstein-Uhlenbeck diffusion given that the system is partially observed via a linear diffusion-type (noisy) sensor. Under Gaussian assumptions, it provides a finite-dimensional exact implementation of the optimal Bayes filter. It is generally the only such finite-dimensional exact instance of the Bayes filter for continuous state-space models. Consequently, this filter has been studied extensively in the literature since the seminal 1961 paper of Kalman and Bucy. The purpose of this work is to review, re-prove and refine existing results concerning the dynamical properties of the Kalman-Bucy filter so far as they pertain to filter stability and convergence. The associated differential matrix Riccati equation is a focal point of this study with a number of bounds, convergence, and eigenvalue inequalities rigorously proven. New results are also given in the form of exponential and comparison inequalities for both the filter and the Riccati ow.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DE120102873
dc.relation.ispartof	SIAM Journal on Control and Optimization	en_US
dc.relation.isbasedon	10.1137/16M1102707	en_US
dc.rights	info:eu-repo/semantics/openAccess
dc.subject.classification	Industrial Engineering & Automation	en_US
dc.title	On the stability of kalman-bucy diffusion processes	en_US
dc.type	Journal Article
utslib.citation.volume	6	en_US
utslib.citation.volume	55	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0906 Electrical and Electronic Engineering	en_US
utslib.for	0913 Mechanical Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Biomedical Engineering
pubs.organisational-group	/University of Technology Sydney/Strength - CHT - Health Technologies
utslib.copyright.status	open_access	*
pubs.issue	6	en_US
pubs.publication-status	Published	en_US
pubs.volume	55	en_US

Abstract:

© 2017 Society for Industrial and Applied Mathematics. The Kalman-Bucy filter is the optimal state estimator for an Ornstein-Uhlenbeck diffusion given that the system is partially observed via a linear diffusion-type (noisy) sensor. Under Gaussian assumptions, it provides a finite-dimensional exact implementation of the optimal Bayes filter. It is generally the only such finite-dimensional exact instance of the Bayes filter for continuous state-space models. Consequently, this filter has been studied extensively in the literature since the seminal 1961 paper of Kalman and Bucy. The purpose of this work is to review, re-prove and refine existing results concerning the dynamical properties of the Kalman-Bucy filter so far as they pertain to filter stability and convergence. The associated differential matrix Riccati equation is a focal point of this study with a number of bounds, convergence, and eigenvalue inequalities rigorously proven. New results are also given in the form of exponential and comparison inequalities for both the filter and the Riccati ow.

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http://hdl.handle.net/10453/127196